The finite index basis property

Berthé, Valérie; De Felice, Clelia; Dolce, Francesco; Leroy, Julien; Perrin, Dominique; Reutenauer, Christophe et Rindone, Giuseppina (2015). « The finite index basis property ». Journal of Pure and Applied Algebra, 219(7), pp. 2521-2537.

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Résumé

We describe in this paper a connection between bifix codes, symbolic dynamical systems and free groups. This is in the spirit of the connection established previously for the symbolic systems corresponding to Sturmian words. We introduce a class of sets of factors of an infinite word with linear factor complexity containing Sturmian sets and regular interval exchange sets, namely the class of tree sets. We prove as a main result that for a uniformly recurrent tree set S, a finite bifix code X on the alphabet A is S-maximal of S-degree d if and only if it is the basis of a subgroup of index d of the free group on A.

Type:	Article de revue scientifique
Mots-clés ou Sujets:	bifix codes, Sturmian sets
Unité d'appartenance:	Faculté des sciences > Département de mathématiques
Déposé par:	Christophe Reutenauer
Date de dépôt:	27 avr. 2016 19:59
Dernière modification:	19 mai 2016 18:16
Adresse URL :	http://archipel.uqam.ca/id/eprint/8350

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